George Gray
07/15/2023 · High School
Kevin bought a \( 7 \frac{2}{3} \) inches tall model of the Statue of Liberty. The scale used for the model was \( \frac{2}{3} \) inch \( =4 \) meters. What is the actual height, in melers, of the Statue of Liberty? Explain how you solved the question.
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Step-by-step Solution
To find the actual height of the Statue of Liberty, we need to set up a proportion using the scale given in the problem.
Given:
- The model of the Statue of Liberty is \( 7 \frac{2}{3} \) inches tall.
- The scale used for the model is \( \frac{2}{3} \) inch = 4 meters.
Let's denote the actual height of the Statue of Liberty as \( x \) meters.
We can set up the proportion as follows:
\[ \frac{7 \frac{2}{3}}{\frac{2}{3}} = \frac{x}{4} \]
Now, we can solve for \( x \) to find the actual height of the Statue of Liberty.
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{7\frac{2}{3}}{\frac{2}{3}}=\frac{x}{4}\)
- step1: Simplify:
\(\frac{23}{2}=\frac{x}{4}\)
- step2: Swap the sides:
\(\frac{x}{4}=\frac{23}{2}\)
- step3: Multiply both sides of the equation by \(4:\)
\(\frac{x}{4}\times 4=\frac{23}{2}\times 4\)
- step4: Multiply the terms:
\(x=\frac{23\times 4}{2}\)
- step5: Evaluate:
\(x=46\)
The actual height of the Statue of Liberty is 46 meters.
Quick Answer
The actual height of the Statue of Liberty is 46 meters.
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